In this paper we present an abstract nonsmooth optimization problem for which we recall existence and uniqueness results. We show a numerical scheme to approximate its solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This problem leads to a hemivariational inequality which we solve numerically. Finally, we compare three computational methods of solving contact mechanical problems: direct optimization method, augmented Lagrangian method and primal-dual active set strategy.

翻译：本文提出一个抽象非光滑优化问题，回顾其存在性与唯一性结果，并展示逼近其解的数值方案。随后将该理论应用于描述弹性体与基础摩擦接触的静态接触问题示例，该问题导出半变分不等式并通过数值求解。最后，我们比较求解接触力学问题的三种计算方法：直接优化法、增广拉格朗日法与原始-对偶活动集策略。